Math 3 Unit 1: Functions and Inverses

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vertex form

The ____________ of a quadratic function is given by. f (x) = a(x - h)2 + k, where (h, k) is the vertex of the parabola.

decreasing

The graph of a function goes down on a portion of its domain when viewed from left to right.

range

The set of all possible output values of a function

standard form

The simplest way to show a number using digits.

maximum

The y-value of the highest point on the graph of a function

minimum

The y-value of the lowest point on the graph of a function

exponential function

f(x)=2^x domain: (-∞, ∞) range: [0, ∞)

step function

f(x)=[x]

standard form of any function

f(x)=a[b(x-h)]+k

cosine function

f(x)=cos(x) domain: (-∞, ∞) range: [-1, 1]

log rhythmic function (inverse exponential)

f(x)=log(x) domain: (0, ∞) range: (-∞, ∞)

sine function

f(x)=sin(x) domain: (-∞, ∞) range: [-1, 1]

linear function

f(x)=x domain: (-∞, +∞) range: (-∞, +∞)

quadratic function

f(x)=x^2 domain: (-∞, ∞) range: [0, ∞)

cubic function

f(x)=x^3 domain: (-∞, ∞) range: (-∞, ∞)

quartic function

f(x)=x^4 domain: (-∞, ∞) range: [0, ∞)

absolute value function

f(x)=|x| domain: (-∞, ∞) range: [0, ∞)

square root function

f(x)=√x domain: [0, ∞) range: [0, ∞)

increasing

from left to right, the graph goes up.

odd function

graph is symmetric with respect to the origin; f(-x)=-f(x)

even function

graph is symmetric with respect to the y-axis; f(-x)=f(x)

reflection over x-axis

negative (a) value

reflection over y-axis

negative (b) value

shift right

negative (h) value

shift down

negative (k) value

inverse of a function

opposite of the function (switch x and y)

shift left

positive (h) value

shift up

positive (k) value

end behavior

the behavior of the graph of a function as x approaches positive infinity or negative infinity

x-intercept

the x-coordinate of a point where a graph crosses the x-axis

y-intercept

the y-coordinate of a point where a graph crosses the y-axis

vertical compression

0<a<1 (wider)

horizontal stretch

0<b<1 (wider)

axis of symmetry

A line that divides a plane figure or a graph into two congruent reflected halves

relative maximum

A point on the graph of a function where no other nearby points have a greater y-coordinate.

relative minimum

A point on the graph of a function where no other nearby points have a lesser y-coordinate.

vertex

A point where two or more straight lines meet.

vertical stretch

a>1 (narrow)

domain

all the possible x-values of a function

horizontal compression

b>1 (narrow)

inverse function

f(x)= 1/x domain: (-∞, 0) U (0, ∞) range: (-∞, 0) U (0, ∞)


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